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| Author | : Mathieu Anel |
| Publisher | : Cambridge University Press |
| Total Pages | : 601 |
| Release | : 2021-04 |
| Genre | : Mathematics |
| ISBN | : 1108490638 |
In this graduate-level book, leading researchers explore various new notions of 'space' in mathematics.
| Author | : Mathieu Anel |
| Publisher | : |
| Total Pages | : 900 |
| Release | : 2020-11-30 |
| Genre | : Mathematics |
| ISBN | : 9781108854368 |
| Author | : Mathieu Anel |
| Publisher | : Cambridge University Press |
| Total Pages | : 437 |
| Release | : 2021-04 |
| Genre | : Mathematics |
| ISBN | : 110849062X |
In this graduate-level book, leading researchers explore various new notions of 'space' in mathematical physics.
| Author | : Mathieu Anel |
| Publisher | : Cambridge University Press |
| Total Pages | : 602 |
| Release | : 2021-04-01 |
| Genre | : Mathematics |
| ISBN | : 1108848214 |
After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. The chapters in this volume cover a broad range of topics in mathematics, including diffeologies, synthetic differential geometry, microlocal analysis, topos theory, infinity-groupoids, homotopy type theory, category-theoretic methods in geometry, stacks, derived geometry, and noncommutative geometry. It is addressed primarily to mathematicians and mathematical physicists, but also to historians and philosophers of these disciplines.
| Author | : Tim Maudlin |
| Publisher | : |
| Total Pages | : 374 |
| Release | : 2014-02 |
| Genre | : Mathematics |
| ISBN | : 0198701306 |
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
| Author | : Max Dickmann |
| Publisher | : Cambridge University Press |
| Total Pages | : 652 |
| Release | : 2019-03-21 |
| Genre | : Mathematics |
| ISBN | : 1107146720 |
Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.
| Author | : Garret Sobczyk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 373 |
| Release | : 2012-10-26 |
| Genre | : Mathematics |
| ISBN | : 0817683852 |
The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.
| Author | : Gerard Buskes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 321 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461206650 |
gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.
| Author | : Melvin Hausner |
| Publisher | : Courier Dover Publications |
| Total Pages | : 417 |
| Release | : 2018-10-17 |
| Genre | : Mathematics |
| ISBN | : 0486835391 |
A fascinating exploration of the correlation between geometry and linear algebra, this text portrays the former as a subject better understood by the use and development of the latter rather than as an independent field. The treatment offers elementary explanations of the role of geometry in other branches of math and science — including physics, analysis, and group theory — as well as its value in understanding probability, determinant theory, and function spaces. Outstanding features of this volume include discussions of systematic geometric motivations in vector space theory and matrix theory; the use of the center of mass in geometry, with an introduction to barycentric coordinates; axiomatic development of determinants in a chapter dealing with area and volume; and a careful consideration of the particle problem. Students and other mathematically inclined readers will find that this inquiry into the interplay between geometry and other areas offers an enriched appreciation of both subjects.
| Author | : Jeffrey R. Weeks |
| Publisher | : CRC Press |
| Total Pages | : 405 |
| Release | : 2001-12-12 |
| Genre | : Mathematics |
| ISBN | : 0203912667 |
Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.
